Pith Number

pith:ISB7EYBD

pith:2016:ISB7EYBDNIDVRH4EKHZEYPLNQO

not attested not anchored not stored refs pending

A generalization of a theorem of Hoffman

Jack H. Koolen, Jae Young Yang, Qianqian Yang

arxiv:1612.07085 v2 · 2016-12-21 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ISB7EYBDNIDVRH4EKHZEYPLNQO}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:11:19.085512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4483f260236a07589f8451f24c3d6d83a758572921fb1401750d98510a9702d5

Aliases

arxiv: 1612.07085 · arxiv_version: 1612.07085v2 · doi: 10.48550/arxiv.1612.07085 · pith_short_12: ISB7EYBDNIDV · pith_short_16: ISB7EYBDNIDVRH4E · pith_short_8: ISB7EYBD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ISB7EYBDNIDVRH4EKHZEYPLNQO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4483f260236a07589f8451f24c3d6d83a758572921fb1401750d98510a9702d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8978583f72598890c4ccbaef340803e3ef6682954baeb40449adbc0c4883faa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-21T13:04:05Z",
    "title_canon_sha256": "93f494471f0d563d72a5da5fc19dae98f88b3db44d1a4733b811619586abcbf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07085",
    "kind": "arxiv",
    "version": 2
  }
}